A366966 - OEIS

%I #16 Nov 11 2023 00:15:31

%S 90,109,190,209,290,309,390,409,490,509,590,609,690,709,790,809,890,

%T 900,901,902,903,904,905,906,907,908,909,910,920,930,940,950,960,970,

%U 980,990,1009,1019,1029,1039,1049,1059,1069,1079,1089,1090,1091,1092,1093,1094,1095

%N Numbers whose difference between the largest and smallest digits is equal to 9.

%C The number of n-digit terms of this sequence is 9*10^(n-1) - 17*9^(n-1) + 8^n.

%t Select[Range[1095],Max[d=IntegerDigits[#]]-Min[d]==9 &]

%o (Python)

%o def ok(n): return max(d:=list(map(int, str(n))))-min(d) == 9

%o print([k for k in range(1100) if ok(k)]) # _Michael S. Branicky_, Oct 30 2023

%o (Python)

%o from itertools import chain, count, islice, combinations_with_replacement

%o from sympy.utilities.iterables import multiset_permutations

%o def A366966_gen(): # generator of terms

%o     return chain.from_iterable(sorted(int(''.join(str(d) for d in t)) for c in combinations_with_replacement(range(10),l) for t in multiset_permutations((0,9)+c) if t[0]) for l in count(0))

%o A366966_list = list(islice(A366966_gen(),30)) # _Chai Wah Wu_, Nov 10 2023

%o (PARI) isok(n) = my(d=digits(n)); vecmax(d) - vecmin(d) == 9; \\ _Michel Marcus_, Nov 05 2023

%Y Cf. A037904.

%Y Cf. A010785 (difference = 0), A366958 (difference = 1), A366959 (difference = 2), A366960 (difference = 3), A366961 (difference = 4), A366962 (difference = 5), A366963 (difference = 6), A366964 (difference = 7), A366965 (difference = 8).

%K nonn,base,easy

%O 1,1

%A _Stefano Spezia_, Oct 30 2023